Differential equation models for tumor growth dynamics
Pranay Kathadepranay.p.kathade@gmail.comRockwell Automation India Pvt. Ltd.Pune, Maharashtra, 411057, IndiaView full profile → , *Smita GambhireCorresponding authorsmitagambhire@csmu.ac.inDepartment of Computer Science & Information Technology Chhatrapati Shivaji Maharaj UniversityNavi Mumbai, Maharashtra, 410206, IndiaView full profile → , Swati Varmaswati.varma@vcet.edu.inDepartment of Computer Engineering Vidyavardhini’s College of Engineering and TechnologyVasai-Virar, Maharashtra, 401202, IndiaView full profile → , Sheetal Patilsheetalsp2105@gmail.comDepartment of Electronics and Computer Science Vidyalankar Institute of Technology Wadala EastDepartment of Electronics and Computer Science Vidyalankar Institute of Technology Vidyalankar College Marg Wadala EastMumbai, Maharashtra, 400037, IndiaView full profile → , Sardor Sabirovsabirov_sardor@mamunedu.uzDepartment of General Professional Sciences Mamun UniversityKhiva, 220900, UzbekistanView full profile → , Shivkumar Karalesjkarale@gmail.comDepartment of Computer Technology Yeshwantrao Chavan College of EngineeringNagpur, Maharashtra, 441110, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Mar 2025
- Published Online:
- 18 Mar 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2509
- Pages:
- 729–737
Abstract
Keywords
Subject Classifications
References
[1] J. Lee and E. Kim, “Ordinary differential equation model of cancer-associated fibroblast heterogeneity predicts treatment outcomes,” npj Systems Biology and Applications, vol. 11, pp. 96 (2025), doi: 10.1038/s41540-025-00578-y.
[2] H. Murphy, H. Jaafari, and H. M. Dobrovolny, “Differences in predictions of ODE models of tumor growth: A cautionary example,” BMC Cancer, vol. 16, pp. 163 (2016), doi: 10.1186/s12885-016-2164-x.
[3] Muskan and S. S. Chauhan, “A theoretical approach to find the solution of population based mathematical model,” Journal of Interdisciplinary Mathematics, vol. 27, no. 8, pp. 1735–1740 (2024), doi: 10.47974/JIM-2035.
[4] A. Yin, D. J. A. R. Moes, J. G. C. van Hasselt, J. J. Swen, and H. J. Guchelaar, “A review of mathematical models for tumor dynamics and treatment resistance evolution of solid tumors,” CPT: Pharmacometrics & Systems Pharmacology, vol. 8, no. 10, pp. 720–737 (Oct. 2019), doi: 10.1002/psp4.12450.
[5] M. B. A. Mansour and A. H. Abobakr, “Stochastic differential equation models for tumor population growth,” Chaos, Solitons & Fractals, vol. 164, pp. 112738 (2022), doi: 10.1016/j.chaos.2022.112738.
[6] S. A. Alharbi and A. S. Rambely, “A new ODE-based model for tumor cells and immune system competition,” Mathematics, vol. 8, pp. 1285 (2020), doi: 10.3390/math8081285.
[7] C. A. Valentim, J. A. Rabi, and S. A. David, “Cellular-automaton model for tumor growth dynamics: Virtualization of different scenarios,” Computers in Biology and Medicine, vol. 153, pp. 106481 (2023), doi: 10.1016/j.compbiomed.2022.106481.
[8] D. Motwani, V. Chitre, V. Bhosale, M. M. Nashipudmath, S. Shinde, and A. Nerurkar, “Implementing secure elliptic curve cryptography for blockchain-based financial transactions,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 29, no. 2-A, pp. 617–627 (2026), doi: 10.47974/JDMSC-2504.
[9] S. Bhattacharya, L. Indise, N. Pandey, B. M. Nanche, S. Ramakrishna, and G. Sethi, “Analyzing the performance of wireless sensor networks using polynomial cryptography methods,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 29, no. 2-A, pp. 563–570 (2026), doi: 10.47974/JDMSC-2497.
[10] M. A. A. Sheela, G. Nikhitha, G. Chennakesavulu, D. M. Kumar, and K. M. Kumar, “Early stage detection of lung cancer using ensemble classification techniques,” International Journal of Advanced Computer Engineering and Communication Technology (IJACECT), vol. 14, no. 1, pp. 40–47 (Apr. 2025).
[11] G. Debnath, B. Vasu, R. S. R. Gorla, O. A. Beg, and T. A. Beg, “Integrating mathematical models in clinical oncology: Enhancing therapeutic strategies,” Archives of Pharmacology and Therapeutics, vol. 7, no. 1, pp. 1–27 (2025).
[12] N. B. Pokale, P. Praveen, Y. Sood, V. Kumar, N. Vairaperumal, and V. K. Vijaya, “Exploring the integration of discrete mathematics and applied algebra in designing robust network architectures for IoT,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 29, no. 2-B, pp. 877–884 (2026), doi: 10.47974/JDMSC-2538.




